In wavelength division multiplexed (WDM) optical communication systems, a number of different optical carrier wavelengths are separately modulated with data to produce modulated optical signals. The modulated optical signals are combined into an aggregate signal and transmitted over an optical transmission path to a receiver. The receiver detects and demodulates the data.
One type of modulation that may be used in optical communication systems is phase-shift keying (PSK). According to different variations of PSK, data is transmitted by modulating the phase of an optical wavelength such that the phase or phase transition of the optical wavelength forms a symbol representing one or more bits. Amplitude-shift keying (ASK) is another type of modulation format wherein data is transmitted by modulating the amplitude of an optical signal such that the amplitude or amplitude transition of the signal forms a symbol representing one or more bits. Amplitude-shift keying and phase-shift keying may be combined to provide an amplitude and phase-shift keying (APSK) format. In an APSK signal, information is modulated using a combination of phase-shift keying and amplitude-shift keying, for example, to encode multiple bits per symbol.
APSK formats may have a square or circular signal constellation. A signal constellation is a predetermined plan or map indicating how information bits correspond to associated symbols modulated on an optical signal. The constellation is typically represented as a two-dimensional scatter diagram in the complex plan. The real and imaginary axes of the complex plane often called the in-phase, or I-axis, and the quadrature, or Q-axis, respectively. For a particular modulation format, the constellation identifies the exact information bits that correspond to each symbol (having real and imaginary values) modulated on an optical wavelength. As used herein a “square constellation” is a constellation wherein the two-dimensional scatter diagram in the complex plane forming the constellation has a square shape with constellation points arranged in a single square or multiple squares having a common center. As used herein a “circular constellation” is a constellation wherein the two-dimensional scatter diagram in the complex plane forming the constellation has a circular shape with constellation points arranged in a single ring or concentric rings.
One type of APSK format with a square signal constellation is a quadrature amplitude modulation (QAM) format. Although a QAM format may be broadly viewed as a format wherein data is represented using PSK with or without ASK, QAM formats using both PSK and ASK and having a square constellation are common. For example, a conventional 16-QAM modulation format having a square constellation uses phase shift keying and amplitude shift keying to represent four bits per symbol.
APSK formats with circular signal constellations may be described as M-APSK formats where M=2m, and each symbol represents m bits. For example, a 16-APSK modulation format may be used to encode 4 bits per symbol and 64-APSK may be used to encode 6 bits per symbol.
Coded modulation has been used with APSK formats to compensate for signal degradation contributed by different sources when an optical signal is transmitted over long distances. Coded modulation involves use of a forward error correction (FEC) code. FEC is essentially the incorporation of a suitable code into a data stream at the transmitter. The transmitter receives a data stream and encodes the data stream using an FEC encoder that introduces some redundancy in the binary information sequence of the data stream. The receiver receives the encoded data and runs it through an FEC decoder to detect and correct errors. Examples of coded modulation QAM schemes are described in U.S. Pat. No. 9,407,398 and U.S. Pat. No. 9,397,786, the teachings of which are hereby incorporated herein by reference.
Constellation shaping is another technique used to improve receiver sensitivity by providing a signal-to-noise (SNR) gain in optical systems. In general, constellation shaping involves transmitting lower energy signals more often than higher energy signals. Geometric constellation shaping and probabilistic constellation shaping are two known techniques. In geometric shaping, the constellation points are not uniformly distributed but are equi-probable. In probabilistic constellation shaping, the constellation points are provided on a uniform grid but with constellation points having different probabilities depending on the constellation point energy.